Resonant MEMS

Part of the AMN book series, this book covers the principles, modeling and implementation as well as applications of resonant MEMS from a unified viewpoint. It starts out with the fundamental equations and phenomena that govern the behavior of resonant MEMS and then gives a detailed overview of their implementation in capacitive, piezoelectric, thermal and organic devices, complemented by chapters addressing the packaging of the devices and their stability. The last part of the book is devoted to the cutting-edge applications of resonant MEMS such as inertial, chemical and biosensors, fluid properties sensors, timing devices and energy harvesting systems.

Autorentext
Oliver Brand is Professor of Bioengineering and Microelectronics/Microsystems at Georgia Institute of Technology, Atlanta, USA. He received his diploma degree in Physics from Technical University Karlsruhe, Germany, in 1990, and his PhD from ETH Zurich, Switzerland, in 1994. Between 1995 and 2002, he held research and teaching positions at the Georgia Institute of Technology (1995-1997) and ETH Zurich (1997-2002). Oliver Brand's research interest lies in the areas of CMOS-based micro- and nanosystems, MEMS fabrication technologies, and microsystem packaging.

Isabelle Dufour is Professor of Electrical Engineering at the University of Bordeaux, France. She received the PhD and habilitation degrees in Engineering Sciences from the University of Paris-Sud, Orsay, France, in 1993 and 2000, respectively. Isabelle Dufour was a CNRS research fellow from 1994 to 2007, first in Cachan working on the modeling of electrostatic actuators such as micromotors and micropumps and after 2000 in Bordeaux working on microcantilever-based chemical sensors. Her research interests are mainly in the areas of sensors for chemical detection, rheological measurements and materials characterization.

Stephen M. Heinrich is Professor of Civil Engineering at Marquette University, Wisconsin, USA. He earned his MSc and PhD degrees from the University of Illinois after which he joined the faculty at Marquette University. Stephen Heinrich's research is focused on structural mechanics applications in microelectronics packaging and the development of new analytical models for predicting and enhancing the performance of cantilever-based chemical sensors. The work performed by Stephen Heinrich and his colleagues has resulted in over 100 publications and presentations and three best-paper awards from IEEE and ASME.

Fabien Josse is Professor in the Department of Electrical and Computer Engineering and the Department of Biomedical Engineering at Marquette University, Wisconsin, USA. He received the MSc and PhD degrees in Electrical Engineering from the University of Maine, and belongs to the Marquette University faculty since 1982. His research interests include solid state sensors, acoustic wave sensors and MEMS devices for liquid-phase biochemical sensor applications, investigation of novel sensor platforms, and smart sensor systems.

Klappentext
Resonant microelectromechanical systems (MEMS) are characterized by sub-millimeter-sized components that are able to oscillate. Depending on the actuation method, these resonant MEMS are implemented, e.g., as electrostatic, electrothermal, magnetostatic or piezoelectric devices. The distinct characteristics of these devices such as a wide frequency range, favorable signal-tonoise ratios, reliability, low power consumption and small size make them useful for a variety of applications ranging from sensors to timing devices.

The book covers the principles, modeling and implementation as well as applications of resonant MEMS from a unified viewpoint. It starts out with the fundamental equations and phenomena that govern the behavior of resonant MEMS and then gives a detailed overview of their implementation in capacitive, piezoelectric, thermal and organic devices, complemented by chapters addressing the packaging of the devices and their stability. The last part of the book is devoted to the cutting-edge applications of resonant MEMS such as inertial, chemical and biosensors, fl uid properties sensors, and energy harvesting systems.

Inhalt

Series editor's preface XV

Preface XVII

About the Volume Editors IX

List of Contributors XXI

Part I: Fundamentals 1

1 Fundamental Theory of Resonant MEMS Devices 3
Stephen M. Heinrich and Isabelle Dufour

1.1 Introduction 3

1.2 Nomenclature 4

1.3 Single-Degree-of-Freedom (SDOF) Systems 5

1.3.1 Free Vibration 6

1.3.2 Harmonically Forced Vibration 8

1.3.3 Contributions to Quality Factor from Multiple Sources 13

1.4 Continuous Systems Modeling: Microcantilever Beam Example 14

1.4.1 Modeling Assumptions 15

1.4.2 Boundary Value Problem for a Vibrating Microcantilever 16

1.4.3 Free-Vibration Response of Microcantilever 17

1.4.4 Steady-State Response of a Harmonically Excited Microcantilever 19

1.5 Formulas for Undamped Natural Frequencies 22

1.5.1 Simple Deformations (Axial, Bending, Twisting) of 1D Structural Members: Cantilevers and Doubly Clamped Members (Bridges) 23

1.5.1.1 Axial Vibrations (Along x-Axis) 23

1.5.1.2 Torsional Vibrations (Based on h b) (Twist About x-Axis) 24

1.5.1.3 Flexural (Bending) Vibrations 24

1.5.2 Transverse Deflection of 2D Structures: Circular and Square Plates with Free and Clamped Supports 25

1.5.3 Transverse Deflection of 1D Membrane Structures (Strings) 25

1.5.4 Transverse Deflection of 2D Membrane Structures: Circular and Square Membranes under Uniform Tension and Supported along Periphery 26

1.5.5 In-Plane Deformation of Slender Circular Rings 26

1.5.5.1 Extensional Modes 26

1.5.5.2 In-Plane Bending Modes 26

1.6 Summary 27

Acknowledgment 27

References 27

2 Frequency Response of Cantilever Beams Immersed in Viscous Fluids 29
Cornelis Anthony van Eysden and John Elie Sader

2.1 Introduction 29

2.2 Low Order Modes 30

2.2.1 Flexural Oscillation 30

2.2.2 Torsional Oscillation 36

2.2.3 In-Plane Flexural Oscillation 37

2.2.4 Extensional Oscillation 37

2.3 Arbitrary Mode Order 38

2.3.1 Incompressible Flows 38

2.3.2 Compressible Flows 46

2.3.2.1 Scaling Analysis 47

2.3.2.2 Numerical Results 48

References 51

3 Damping in Resonant MEMS 55
Shirin Ghaffari and Thomas William Kenny

3.1 Introduction 55

3.2 Air Damping 56

3.3 Surface Damping 59

3.4 Anchor Damping 61

3.5 Electrical Damping 63

3.6 Thermoelastic Dissipation (TED) 64

3.7 Akhiezer Effect (AKE) 66

References 69

4 Parametrically Excited Micro- and Nanosystems 73
Jeffrey F. Rhoads, Congzhong Guo, and Gary K. Fedder

4.1 Introduction 73

4.2 Sources of Parametric Excitation in MEMS and NEMS 74

4.2.1 Parametric Excitation via Electrostatic Transduction 75

4.2.2 Other Sources of Parametric Excitation 77

4.3 Modeling the Underlying DynamicsVariants of the Mathieu Equation 77

4.4 Perturbation Analysis 79

4.5 Linear, Steady-State Behaviors 80

4.6 Sources of Nonlinearity and Nonlinear Steady-State Behaviors 81

4.7 Complex Dynamics in Parametrically Excited Micro/Nanosystems 84

4.8 Combined Parametric and Direct Excitations 85

4.9 Select Applications 85

4.9.1 Resonant Mass Sensing 85

4.9.2 Inertial Sensing 86

4.9.3 Micromirror Actuation 87

4.9.4 Bifurcation Control 88

4.10 Some Parting Thoughts 89

Acknowledgment 89

References 89

5 Finite ElementModeling of Resonators 97
Reza Abdolvand, Jonathan Gonzales, and Gavin Ho

5.1 Introduction to Finite Element Analysis 97

5.1.1 Mathematical Fundamentals 97

5.1.1.1 Static Problems 98 5.1.1.2 Dynamic Problems (Mod...